Section: New Results

Analysis and Transformation of Parallel Programs

Participants : Albert Cohen [Inria/PARKAS] , Alain Darte, Paul Feautrier, Abdoulaye Gamatie [CNRS/LIRMM] , Laure Gonnord, Alain Ketterlin [Inria/CAMUS] , Sanjay Rajopadhye [Colorado State University] , Vijay Saraswat [IBM Research] , Eric Violard [Inria/CAMUS] , Tomofumi Yuki.

While, historically, Compsys has applied polyhedral analysis to sequential programs, it was recently realized that it also applies to parallel programs, with the aim of checking their correctness or improving their performance. The prospect of having to program exascale architectures, with their millions of cores, has led to the development of new programming languages, whose objective is to increase the programmer productivity. Compsys has applied polyhedral techniques to synchronous languages (see  [25] , [26] and previous activity reports), to IBM's high-productivity language X10, and, in the context of the ManycoreLabs project, to a streaming language, OpenStream, developed by Albert Cohen's group.

X10 is based on the creation of independent activities (light-weight threads), which can synchronize either by a generalization of the fork/join scheme, or with clocks, an improved version of the familiar barriers. X10 is deadlock-free by construction but it is the programmer responsibility to insure determinism by a proper use of synchronizations. Non-determinism bugs may have a very low occurrence probability thus be very difficult to detect by testing, hence the interest for detecting races at compile time. In collaboration with CSU (S. Rajopadhye, T. Yuki) and IBM (V. Saraswat), we extended array dataflow analysis to polyhedral clock-free X10 programs  [29] . We have been working on clocked programs too: race detection becomes undecidable  [30] , but realistic problems may still be solved by heuristics.

As a side-effect of this work, we have shown in cooperation with Eric Violard and Alain Ketterlin (Inria Team Camus, Strasbourg) that clocks can be removed and replaced by async/finish constructs without modifying the program semantics [6] . While this transformation incurs a large overhead for general programs, in the polyhedral case the overhead is negligible, thus improving the program performance.

In contrast to X10, OpenStream is deterministic by construction, but may have deadlocks. A usual way of disproving deadlocks is by exhibiting a schedule for the program operations, a well-known problem for polyhedral programs, where dependences can be described by affine constraints. In the case of OpenStream, communications use one-dimensional channels and, in a form of linearization, give rise to polynomial dependences for polyhedral OpenStream codes. In a ManycoreLabs project deliverable (see Section  7.1 ), we have formalized the problem and proved that deadlock detection is undecidable in general.